In many manufacturing processes parts or compositions of matter are made which are required to fall within certain specifications. The specifications state the important features or characteristics required to produce a product of a desired quality. Those specifications typically state dimensions of a product or elements of a composition, but could also be physical or chemical properties. Each characteristic has a nominal value corresponding to the preferred value of the specified characteristic. Nearly always, a product having the specified characteristic within a certain range or tolerances of the nominal value is considered acceptable.
In order to assure that products fall within specifications, manufacturers typically take samples from the production line which are analyzed by quality control inspectors. The number of samples taken and when they are taken are usually specified by the manufacturer based upon known statistical sampling techniques or past manufacturing experience.
Should the quality control inspector analyze a sample and find that a particular characteristic is outside the specified tolerance limits he will normally shut the manufacturing line down, and make the necessary corrections to bring the product within the specification. However, in the event that the inspector finds that all characteristics of the sample are within the tolerances specified for the product, he will simply note his findings in a log and allow the manufacturing process to continue to run. This data could also be entered into a computer database. Conventionally, the data has also been reproduced in tables or graphs which are almost always created after completion of the production run. Sometimes average values and standard deviations are computed and displayed in tables or graphs. Prior to the present invention the graphs have been either standard plots of datapoints on an x, y coordinate or histograms.
Even though all of the samples taken by the quality control inspector are within the tolerance levels specified, that is no guarantee that every product manufactured over a production run will be within the specified tolerance limits. Edward Demming and its followers have developed a technique known as statistical process control, or SPC, which applies certain equations to the readings taken by the quality control inspector. Statistical process control generates a set of numbers conventionally identified by various letters or letter combinations as follows:
x is a single reading or value
x is an average of readings within a cell.
X.sub.avg is an average of all readings. ##EQU1##
R (Range) is the difference between readings within a cell or between cells.
R is the average of all ranges. ##EQU2##
.sigma. (sigma) is the standard deviation of the distribution of individual values of a process characteristic. ##EQU3##
USL is the abbreviation for upper spec limit.
LSL is the abbreviation for lower spec limit.
C/L control limits (upper & lower) are lines on a control chart used for a basis for judging a process. EQU UCL.times.=X.sub.avg +(A.sub.2 R) EQU LCL.times.=X.sub.avg -(A.sub.2 R)
where E.sub.2 is a constant corresponding to sample size such as 2.66 for a single sample and 1.77 if the sample size is three. EQU UCL.sub.R =D.sub.4 R--specify betw. R,R
where D.sub.4 is a constant corresponding to sample size which constant for a single sample is 3.27 and for sample size of 3 is 2.57.
cp is the inherent capability of a process in relationship to the tolerance. ##EQU4## CpK is the inherent capability in relationship to specification mean. (Most always be viewed from worst case). ##EQU5##
Persons familiar with SPC can use the various statistical results to predict the probably that a product made during a given production run will be outside the accepted tolerances specified for the product. Consequently, many purchasers now require their suppliers to provide statistical process control numbers for each production run or shipment. Additionally, many manufacturers maintain records of these numbers. Several people have attempted to use this historical data to identify trends or to look for standard or recurring values which could indicate either normal operation or particular problems in the manufacturing process. Unfortunately, the volume of data and the manner in which it has been presented and stored have overwhelmed most production managers. Consequently, they have not been able to achieve their objectives. Moreover, prior to the present method statistical process control data has been difficult to use during the production run resulting in a lack of use by most manufacturers during the manufacturing process.
The data collected by the quality control inspectors is often entered into database programs to which various statistical programs can be applied. However, none of these programs have provided much meaningful information to the production manager. Sometimes the inspectors also will graph the data they collect to look for any trends. However, because of the huge amount of data generated during even a single production run, graphs made of that data tend to be too voluminous to be subject to easy comparison. The numbers themselves are even more difficult to analyze. Moreover, when one considers multiple production runs over several days, weeks or months the volume of data is so large that meaningful analyses have not been made. Historical data has not been used to much extent to improve or control subsequent similar production runs or to establish standard values which correspond to normal operation. Consequently, there is need for methods which utilize statistical process control during the manufacturing operation to maintain and improve product quality.